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itel CAMERA Exercise 14c Use i) Which arc subtends ABE? O) Which arc subtends BÊC? Write down two angles equal to BÊC. () Which arc subtends EÂC? ) Write down an angle equal to EÂC. B. E. Fig. 14.23 2 Find the marked angle in each of the following. Where a point O is given it is the centre of the circle. (Hint: make a careful copy of each figure and write in the angles as they are found. Some constructions may be necessary.) (2) (b)

itel CAMERA Exercise 14c Use i) Which arc subtends ABE? O) Which arc subtends BÊC? Write down two angles equal to BÊC. () Which arc subtends EÂC? ) Write down an angle equal to EÂC. B. E. Fig. 14.23 2 Find the marked angle in each of the following. Where a point O is given it is the centre of the circle. (Hint: make a careful copy of each figure and write in the angles as they are found. Some constructions may be necessary.) (2) (b)

Elementary Geometry For College Students, 7e
Elementary Geometry For College Students, 7e
7th Edition
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
ChapterP: Preliminary Concepts
SectionP.CT: Test
Problem 1CT
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# Geometry Problem on Circle Angles and Arcs ## Exercise 14c ### Question 1 Use Fig. 14.23 to answer the following: Given a circle with points A, B, C, D, and E lying on the circumference and chords AB, BC, CD, DE, and AE. **(a) Which arc subtends ∠AΒΕ?** - Answer: Arc AE. **(b) Write down an angle equal to ∠ΑΒΕ.** - Answer: ∠ADE (angles subtended by the same arc are equal). **(c) Which arc subtends ∠BΕC?** - Answer: Arc BC. **(d) Write down two angles equal to ∠ΒΕC.** - Answer: ∠BDC and ∠BAC (angles subtended by the same arc are equal). **(e) Which arc subtends ∠AΕC?** - Answer: Arc AC. **(f) Write down an angle equal to ∠FΑC.** - Answer: ∠EBD (angles subtended by the same arc are equal). ### Figure 14.23 - The diagram features a circle with chords AB, BE, EC, CA, and AD drawn inside it. - The central points of interest are the intersection points on the circumference labeled A, B, C, D, and E. ### Question 2 Find the marked angle in each of the following (two diagrams shown): - **Hints:** - Point O is the center of the circle. - Copy each figure and write in the angles as they are found. Some constructions may be necessary. **(a)** First Circle Diagram (Fig. 14.23): - Diagram shows a circle with a central angle marked as 40°. **(b)** Second Circle Diagram (Fig. 14.23): - Diagram shows a circle with a central angle marked as 58°. Ensure students understand that angles subtended by the same arc in a circle are equal and the relationship between arcs and the angles they subtend.
Transcribed Image Text:# Geometry Problem on Circle Angles and Arcs ## Exercise 14c ### Question 1 Use Fig. 14.23 to answer the following: Given a circle with points A, B, C, D, and E lying on the circumference and chords AB, BC, CD, DE, and AE. **(a) Which arc subtends ∠AΒΕ?** - Answer: Arc AE. **(b) Write down an angle equal to ∠ΑΒΕ.** - Answer: ∠ADE (angles subtended by the same arc are equal). **(c) Which arc subtends ∠BΕC?** - Answer: Arc BC. **(d) Write down two angles equal to ∠ΒΕC.** - Answer: ∠BDC and ∠BAC (angles subtended by the same arc are equal). **(e) Which arc subtends ∠AΕC?** - Answer: Arc AC. **(f) Write down an angle equal to ∠FΑC.** - Answer: ∠EBD (angles subtended by the same arc are equal). ### Figure 14.23 - The diagram features a circle with chords AB, BE, EC, CA, and AD drawn inside it. - The central points of interest are the intersection points on the circumference labeled A, B, C, D, and E. ### Question 2 Find the marked angle in each of the following (two diagrams shown): - **Hints:** - Point O is the center of the circle. - Copy each figure and write in the angles as they are found. Some constructions may be necessary. **(a)** First Circle Diagram (Fig. 14.23): - Diagram shows a circle with a central angle marked as 40°. **(b)** Second Circle Diagram (Fig. 14.23): - Diagram shows a circle with a central angle marked as 58°. Ensure students understand that angles subtended by the same arc in a circle are equal and the relationship between arcs and the angles they subtend.
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